Answer:
Purchase Price = $150 and Total Price = $162
Step-by-step explanation:
Purchase price = Tax Amount / Tax Percentage (as decimal)
Purchase Price = $12 / .08
Purchase Price = $150
Total Price = Purchase Price + Tax
Total Price = 150 + 12 = $162
I hope this helps!
-The Business Man
Let un be the nth Fibonacci number. Prove that the Euclidean algorithm takes precisely n steps to prove that gcd(un+1, un) = 1.
Hello, Please consider the following.
Fibonacci numbers are defined as
[tex]u_0=1\\\\u_1=1\\\\u_{n+2}=u_{n+1}+u_{n} \ for \ n\geq 0[/tex]
Step 1 - The proposition is true for n = 1
[tex]GCD(u_2,u_1) ?\\[/tex]
Let's apply Euclidean algorithm
[tex]u_1=1, u_2=2\\\\u_2=2\times u_1+0 = 2 \times 1 +0[/tex]
This is exactly 1 step and [tex]GCD(u_2,u_1) =1[/tex]
Step 2 - We assume that this is true for k, meaning that the Euclidean algorithm takes precisely k steps to prove that [tex]GCD(u_{k+1},u_{k})=1[/tex]
[tex]u_{k+2}=u_{k+1}+u_k \ and \ 0 < u_k < u_{k+1}[/tex]
So, the first step of the algorithm is
[tex]u_{k+2}=u_{k+1}\times 1 +u_{k}[/tex]
And from now, we need to find [tex]GCD(u_{k+1},u_k)[/tex] which is 1 and takes k steps, by induction Hypothesis. Therefore, it takes k + 1 steps to find [tex]GCD(u_{k+2},u_{k+1})=1[/tex]
Step 3 - Conclusion
We have just proved that the Euclidean algorithm takes precisely n steps to prove that [tex]GCD(u_{n+1},u_{n})=1[/tex]
Thanks
Find the center of this circle by completing the square. x^2+y^2-6x+8y+10=0
Show work
Answer:
Center: (3, - 4)
Step-by-step explanation:
We can start to solve this problem by converting this equation into standard form. In other words, by completing the square --- (1)
Subtract " 10 " from either side of the equation x² + y² - 6x + 8y + 10 = 0
x² + y² - 6x + 8y = - 10
Step 1: Complete the square for the expression " x² - 6x "
Using the quadratic equation ax² + bx + c we know that a = 1, b = - 6, c = 0. Assume that d = b / 2a. We have...
d = - 6 / 2(1) = - 6 / 2 = - 3
Now let's assume that e = c - (b²) / 4a...
e = 0 - (-6)² / 4(1) = 0 - 36 / 4 = 0 - 9 = 9 (Substitute values d and e)
(x - 3)² - 9
Step 2: Respectively we can complete the square for the remaining expression " y² + 8y "
Here a = 1, b = 8, c = 0
d = 8 / 2(1) = 8 / 2 = 4
e = 0 - (8)² / 4(1) = 0 - 64 / 4 = 0 - 16 = - 16 (Substitute values)
(y + 4)² - 16
This leaves us with the expression " (x - 3)² - 9 + (y + 4)² - 16 = - 10. " If we simplify this a bit further it leaves us with the following circle equation. Using this we can identify the center of the circle as well --- (2)
[tex]\mathrm{Standard}\:\mathrm{Circle}\:\mathrm{Equation} : (x - 3)^2 + (y +4)^2 = 15,\\\mathrm{General}\:\mathrm{Form} : (x - h)^2 + (y +k)^2 = r^2,\\\mathrm{Properties} : \mathrm{Center} = (3, - 4), \mathrm{Radius} = \sqrt{15}[/tex]
As you can see our center here is (3, - 4)
slove it this question
Answer:
a = 60°
Step-by-step explanation:
Formula used:
[tex] \red{\boxed {\bold {\tan \: \theta = \cot \: (90\degree - \theta)}}} [/tex]
[tex] \tan \: 30 \degree = \cot \: a \\ \cot \: (90 \degree - 30 \degree) = \cot \: a \\ cot \: 60 \degree = \cot \: a \\ 60 \degree = a \\ \huge \red{ \boxed{ a = 60 \degree}}[/tex]
Hazel graphs a point on a coordinate plane. The point is located 4 units from the x-axis. Which order pair could describe the point that Hazel graphs.
A. (9,5)
B. (3,4)
C. (2,2)
D. (4,1)
Answer: B
Step-by-step explanation: (3, 4) is 4 units above the x-axis
Evaluate: [(- 16) + 4] ÷ [(-2) + 5]
Answer:
We need to evaluate this: [(-16)+4] / [(-2)+5]
First, we do the brackets:
[(-16)+4][(-2)+5][(-16)+4] = -16 + 4 = -12
[(-2) + 5] = -2 + 5 = 3
Now, we only need to divide, as we have calculated both brackets:
-12/3 = -4
(Remember that when dividing a negative number by a positive one, we always obtain a negative)
So the result is -4
A lumber company is making boards that are 2599.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 23 is made, and it is found that they have a mean of 2600.3 millimeters with a standard deviation of 13.0. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?
Answer:
There is no sufficient evidence to support the claim that the boards are either too long or too short
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2599.0[/tex]
The sample size is [tex]n = 23[/tex]
The sample mean is [tex]\= x = 2600.3 \ mm[/tex]
The standard deviation is [tex]\sigma = 13.0[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 2599.0[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 2599.0[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 2600.3 - 2599.0 }{ \frac{13}{ \sqrt{ 23} } }[/tex]
=> [tex]t = 0.3689[/tex]
Now from the normal distribution table the critical value of [tex]\alpha[/tex] is
[tex]Z_{\alpha } = 1.645[/tex]
Hence from the evaluated and obtained value we see that
[tex]t < Z_{\alpha }[/tex]
Hence we fail to reject the null hypothesis
Thus we can conclude that there is no sufficient evidence to support the claim that the boards are either too long or too short
First answer gets Brainlyist
4 lemons are bought for Rs10 and sold 3 Rs10 what is the profit?
Answer:
Rs0.83
Step-by-step explanation:
i hope it helped you.
Create an example of a situation where there is a negative cash flow.
Answer:
when say your expenses are $400 a month but your income is only $350 a month that is -$50 every month so in that case you aren't getting a positive cash flow (which would be making more money than your expenses) So you must be getting a negative cash flow in which you are losing money and going into debt.
Hope this Helps :)
Use the equation to answer the questions. Round both answers to nearest whole number. Y=51.75−1.25X If Y equals 4, what is X?
Answer:
38.2, or 38 1/2
Step-by-step explanation:
Steps for Solving Linear Equation:
4=51.75−1.25x
Swap sides so that all variable terms are on the left hand side.
51.75−1.25x=4
Subtract 51.75 from both sides.
−1.25x=4−51.75
Subtract 51.75 from 4 to get −47.75.
−1.25x=−47.75
Divide both sides by −1.25.
x=−1.25−47.75
Expand −1.25−47.75≈38.2 by multiplying both numerator and the denominator by 100.
x=−125−4775
Reduce the fraction −125−4775≈38.2 to lowest terms by extracting and canceling out −25.
x=5191
insert two fractions between 3/5 and 4/7
(1) 10/12, 5/9 (2) 11/15, 8/9 (3) 10/17, 7/12 (4) 18/10,6/5
The length of a rectangle is 3 units more than the width. Let x = the width.Then ? = the length.
Answer:
Length = X + 3
Step-by-step explanation:
Examples for the length width relationship would go as follows:
Width Length
1 4
2 5
3 6
4 7
Hope this helps!
-TheBusinessMan
Answer:
Length = x + 3
Step-by-step explanation:
Width = x
Length = 3 + Width
So, Length = 3 + x
So, if Width as a number, then Length will be 3 more than that number.
Solve the system of equations using Gaussian elimination.
[tex]4x+y-3z &= 11 \\2x-3y+2z &= 9 \\x+y+z &= -3[/tex]
The solution (with steps) and answer are included in the images below.
Best of Luck!
Two angles are supplementary. All we know is that the smaller angle is 126 degrees fewer than the larger one. Find
the measure of the larger angle.
Answer:
Larger angle= 153°
Smaller angle= 27°
Step-by-step explanation:
Supplementary angles are two angles that add up to 180°
Let the smaller angle= x
Let the larger angle= y
X+y= 180... equation one
Y-126= x..... equation two
(Y-126) +y = 180
2y= 180+126
2y= 306
Y= 153°
Y-126= x.
153-126= x
27°=x
Solve the linear equation for y in terms of x. -8x-y=12
Answer:
1.5
Step-by-step explanation:
Answer: y=-8x -12
Step-by-step explanation:
-8x - y =12 to solve for y add -8x to both sides
+8x +8x
-y = 12 +8x Now divide each side by -1
y = -8x -12
Which of the following is an example of earning income from capital gains?
a hourly employee earning $17 per hour
b. salaried employee earning $56,000 per year
c. selling a car and making a profit of $3,000
d. selling stocks for a total of $5,000
Answer:
C. selling a car and making a profit of $3,000
Step-by-step explanation:
An example of earning income from capital gains is selling a car and making a profit of $3,000 which the correct answer would be an option (C).
What is capital gross?Gross capital formation for a unit or sector is calculated using the total value of gross fixed capital growth, changes in inventories, and asset acquisitions with fewer asset disposals.
As we know, from the meaning of capital gain:
When a capital asset is sold, the rise in value is known as a capital gain.
Selling a car and getting $3,000 in profit is one example of making money through capital gains.
An example of earning income from capital gains is selling a car and making a profit of $3,000
Hence, the answer would be option (C).
Learn more about the capital gross here:
https://brainly.com/question/2948028
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Which of the following expressions is not equivalent to 14?
7x2 2x(-7) 2x7 -7x(-2)
Answer:
in my opition is 2x(-7)
Step-by-step explanation:
hope it help
A researcher wishes to examine the effects of a new medical treatment on
patients with Alzheimer's disease. The researcher plans to examine the
effects on a group of randomly selected subjects. What is wrong with this
design?
Select all that apply.
A. Subjects are not randomly assigned to an experimental group and
control group.
B. A control group is not used.
C. Only one researcher is used.
D. An entire population is not used.
Find a 3-by-3 magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24.
Fill in the magic square.
The required magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24 is | 6 | 8 | 10 |
| 13 | 15 | 17 |
| 20 | 22 | 24 |.
What is a magic square?A magic square is a square grid of numbers, typically integers, where the numbers in each row, column, and diagonal add up to the same constant value.
Here,
To create a magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24, we can follow these steps,
Start by placing the number 15 in the center square of the grid.
Place the number 6 in one corner of the grid. We'll choose the top left corner for this example.
Place the number 24 in the opposite corner. We'll choose the bottom right corner for this example.
Place the remaining numbers in the empty squares of the grid, following these rules:
a. If a square is already occupied, move to the next square in the same direction.
b. If you reach the edge of the grid, wrap around to the other side.
c. If you reach a square that is diagonally adjacent to a previously filled square, move to the next empty square in a clockwise direction.
Using these rules, we can fill in the rest of the grid as follows:
| 6 | 8 | 10 |
| 13 | 15 | 17 |
| 20 | 22 | 24 |
Learn more about magic square here:
https://brainly.com/question/28675556
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Question 61 point
5. Of the 30 girls who tried out for the lacrosse team
at Euclid Middle School, 12 were selected. Of the
40 boys who tried out, 16 were selected. Are the ratios
of the number of students on the team to the number of
students trying out the same for both boys and girls?
How do you know?
I
what type of shape is a square
Answer:
A square is a closed, two dimensional shape with 4 equal sides.
It is also a quadrilateral.
Step-by-step explanation:
none :)
Solve for U. 4(3-U)+U= 22+2U
Step-by-step explanation:
4(3-U)+U = 22+2U
12-4U+U = 22 + 2U
12-5U= 22+2U
10=3U
U = 10/3
U= 3.3
Which statement is true? (Please help)
Answer:
Option (2)
Step-by-step explanation:
From the picture attached,
Angle between HB and FG = 90°
Therefore, HB and FG are perpendicular segments.
HB ⊥ FG
Similarly, angle between HB and AC = 90°
Therefore, both the segments HB and AC will be perpendicular.
HB ⊥ AC
Since FG and AC are both perpendicular to HB.
Therefore, FG║AC.
Option (2) will be the correct option.
State the domain and range for the following relation. Then determine whether the relation represents a function
Choose the correct answer below.
A.) Domain : {Red, Yellow
Range - Color
B.) Domain : {XS, Red, Yellow, 45, A}
Range = {Size, Color, Number, Letter)
C.) Domain : {Size, Color, Number, Letter}
Range : XS, Red, Yellow. 45. A}
D.) Domain : {Size Number, Letter)
Range : XS, 45, A
can someone please help me figure this out i think its B but im not sure
Answer:
Domain: {XS, Red, Yellow, 45, A}
Range: {Size, Color, Number, Letter}
Step-by-step explanation:
The domain of the function shown in the mapping above are all variables that fall under "A word", while the range consists of all variables under "category".
The mapping shows that the relation represents a function, because each domain variable has exactly one range variable. No single domain variable is mapped to two different range variable.
The correct answer is:
Domain: {XS, Red, Yellow, 45, A}
Range: {Size, Color, Number, Letter}
Write an expression to represent the total cost of paint at a rate of $5.75 per ft.? to paint a triangular-shaped mural where the base of the triangle is 22 feet longer than the height
Answer:
C($)= (x²/2 +11x)5.75
Step-by-step explanation:
Let's assume the height= x
The base= x+22
Area= 1/2(base*height).
Area= 1/2((x+22)(x))
Area= x²/2 +11x
Cost per ft= $5.75
Cost for painting the triangular mural C
C($)= (x²/2 +11x)5.75
What is 9+(5x10)+1-(15x2)
Step-by-step explanation:
Answer:30. hope this helps
Answer:
30
Step-by-step explanation:
9+(5x10)+1-(15x2)
Multiply the numbers
9+(50)+1-(30)
9+50+1-30
30
Evaluate the expression when a = -6 and y=2 . a-6y
Answer:
-18
Step-by-step explanation:
So we have the expression:
[tex]a-6y[/tex]
And we want to evaluate it when y=2 and a=-6.
Substitute in these values:
[tex]=(-6)-6(2)[/tex]
Multiply:
[tex]=(-6)-12[/tex]
Subtract:
[tex]=-18[/tex]
Answer:
-18
Step-by-step explanation:
We are given the expression:
[tex]a-6y[/tex]
and asked to evaluate when a= -6 and y=2.
Therefore, we must substitute -6 in for a and 2 in for y.
[tex]a-6y , a=-6, y=2[/tex]
[tex](-6)-6(2)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.
Multiply 6 and 2.
[tex](-6)-(6*2)[/tex]
[tex](-6)-(12)[/tex]
[tex](-6)-12[/tex]
Subtract 12 from -6.
[tex](-6-12)[/tex]
[tex]-18[/tex]
The expression a-6y when evaluated for a=-6 and y=2 is equal to -18.
Kalvin sells bottles of water at baseball games. He pays $0.75 per bottle and $3.78 for the ice to keep the water cold. Let b represent the
number of bottles of water he buys and C represent his total cost.
Which equation shows the relationship between his total cost and the number of bottles?
O A. C = b +0.75
O B. C = b +3.78
OC. C = 0.75 +3.78
OD. C = 3.78b+0.75
Multiply the cost per bottle by the number of bottles and add that to the cost of ice.
Answer : C = 0.75b + 3.78
Answer:
C = 0.75b + 3.78
The ratio of boys to girls in Mrs. Johnson's class is 4 to 5. There are 10 girls in the class. What is the total number of students in Mrs. Johnson's class?
Answer:
i think it would be 18 kids in the class
Step-by-step explanation:
since for every 4 boys there are 5 girls and so it means
so for every 10 girls there would be 8 boys
Tomas works as an underwater photographer. He starts at a position that is 17 feet below sea level. He rises 7 feet, then descends 13 feet to take a photo of a coral reef. Enter an expression to find his position relative to sea level when he took the photo and then evaluate the expression.
Answer:
(-17+7)-13 or -17-13+7
Step-by-step explanation:
Answer:
Step-by-step explanation: -17+7=10-13=-2